Paper proposes a stable update rule in hyperbolic space for better network modeling.
problem Complex network modeling in hyperbolic space.
method Explicit geodesic update rule in hyperbolic space with theoretical convergence guarantees.
result Algorithm convergence rate is better than Euclidean gradient descent and avoids bias.
Geodesic descent optimizes likelihood in dually flat spaces.
problem Maximum likelihood estimation in exponential families.
method m-geodesic and e-geodesic updates on dually flat spaces.
result Geodesic updates can reach maximum likelihood estimator in one step.
Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry. The progress in the last two decades has become impressive, being especially re…
Dissertation tackles geodesic ray transform on Riemannian manifolds.
problem Determining functions from line integrals along geodesics.
method Establishes conditions for unique and stable determination of functions.
result New numerical model for computed tomography imaging created.
In this paper, we first provide an updated survey of the geometry of complex Cartan spaces. New characterizations for some particular classes of complex Cartan spaces are pointed out, e.g. Landsberg-Cartan, strongly Berwald-Cartan and others. We introduce the Cartan-Randers spaces which offer examples of Berwald-Cartan…
SLERP interpolation optimizes dynamic weight rebalancing in AMMs.
problem Optimizing dynamic weight rebalancing in automated market makers (AMMs).
method Riemannian geometry and SLERP interpolation.
result SLERP interpolation minimizes the KL divergence loss in dynamic weight rebalancing.
This paper was first written in 1990, but was never published. In it, the author presents a novel approach to the study of constant curvature spacetimes in 2+1 dimensions. A parameterization of flat 2+1-dimensional domains of dependence is given in terms of measured geodesic laminations. There is also an interesting re…
Paper proposes efficient weight updates for edge nodes with minimal communication.
problem Inefficient and resource-intensive full weight updates for edge nodes.
method Deep partial updating, selecting a subset of weights to update.
result Achieves similar performance with fewer weight updates.
Paper defines new curvature measures for foliated manifolds and proves new theorems.
problem Estimating the diameter and splitting theorems for foliated manifolds.
method Introduced weighted mixed curvatures and new conditions to update estimates.
result Updated estimates of diameter and proved new splitting theorems.
A new update rule for deep reinforcement learning reduces learning variance and variance in reference signals.
problem Learning variance and incorrect reference signals in deep reinforcement learning.
method t-soft update method inspired by student-t distribution, which reduces extreme updates and accelerates similar updates.
result The t-soft update method outperforms conventional methods in terms of return and variance in PyBullet robotics simulations.
Paper proves Jeffrey's update rule minimizes relative entropy.
problem Improving Bayesian learning algorithms.
method More concise proof of Jeffrey's update rule.
result Jeffrey's update rule reduces relative entropy.
New implicit Krasulina's k-PCA update avoids QR-decomposition and improves convergence.
problem Online k-PCA problem with orthonormality constraint.
method Derived an implicit form of Krasulina's update that bypasses orthonormality constraint.
result The new update avoids costly QR-decomposition and yields superior convergence.
AMUSE uses reinforcement learning to predict optimal model updates.
problem Concept drift weakens model performance over time.
method Reinforcement learning in a simulated environment.
result AMUSE proactively recommends updates based on performance improvements.
New updates for β-divergence in convolutional NMF are stable and consistent.
problem Improving the stability and consistency of NMF updates for convolutional data.
method Presented multiplicative updates for β-divergence in closed form. result The new updates are stable and consistent across common β values. Study on distributed coordinate descent with quantized updates for finite precision communication.
problem Finite precision communication limits the accuracy of updates in distributed coordinate descent.
method Introduced a randomized distributed coordinate descent algorithm with quantized updates, derived convergence conditions, and validated with experiments.
result Algorithm with quantized updates converges under certain conditions on the quantization error.
Efficiently updates posterior tree distributions over meta-trees.
problem Updating posterior distributions over meta-trees efficiently.
method Batch updating method for posterior tree distributions.
result More efficient batch updating method.
Unified approach combining gradient descent and multiplicative updates.
problem Combining gradient descent and multiplicative updates for machine learning.
method Introduces hypentropy and a family of matrix-based updates.
result Derives tight regret bounds for the new family of updates.
LD-SGD improves communication in decentralized SGD.
problem Efficiently combining local updates and decentralized communication.
method Proposes LD-SGD integrating local updates and decentralized SGD, with a convergence analysis.
result LD-SGD converges to a critical point for non-convex objectives with non-identically distributed data.
Paper extends 2D β-CNMF with exact multiplicative updates.
problem Improving nonnegative matrix factor deconvolution for 2D data.
method Derives exact multiplicative updates for β-CNMF factors. result The updates lead to monotonically decreasing β-divergence. The paper examines how updates to probabilistic models influence behavior based on evidence.
problem Understanding how updates to probabilistic models influence behavior based on evidence.
method Study of KL-regularized soft updates as Bayesian posterior updates within a single probabilistic model.
result Posterior updates determine relative incentives but not absolute rewards, which are ambiguous up to context-specific baselines.
Paper improves policy updates in reinforcement learning to speed up learning.
problem Slow learning and unlearning in policy optimization.
method Introduces a novel gradient update and a modified policy update.
result Proves modified policy update converges to global optimality.
Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.
problem Nonlinear and non-Gaussian Bayesian updates for complex systems.
method Combines Kalman filtering for observed components and kernel density estimation for unobserved components, with subsampling and clustering.
result Reduces estimation errors in highly nonlinear scenarios compared to standard linear updates.
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
Paper compresses neural network weight-updates for image artifacts removal.
problem Efficiently compressing neural network weight-updates for image artifacts removal.
method Fine-tuning a pre-trained artifact removal network on target data with a compression objective that encourages sparse and quantized weight-updates.
result Achieves reconstruction quality comparable to traditional codecs at comparable bitrates.
Round spheres are uniquely characterized by half-geodesics.
problem Characterizing round spheres in Riemannian geometry.
method Establishing that Riemannian spheres with specific geodesic properties are round.
result Riemannian spheres with all geodesics closed and many half-geodesics are round.
End-to-end encrypted neural network improves privacy and compression in federated learning.
problem Privacy and bandwidth issues in gradient updates transmission in federated learning.
method Proposes an end-to-end encrypted neural network to encode and decode gradient updates.
result Effective privacy protection and data compression with minimal accuracy loss.
EnKF's update is shown to be similar to Matheron's method in Gaussian process regression.
problem Data assimilation in high-dimensional systems.
method Empirical Matheron update applied to EnKF.
result Ensemble Kalman Filter's update is equivalent to an empirical Matheron update.
Improved HGF networks avoid negative precision errors in volatility updates.
problem Negative posterior precision errors in volatility-coupled nodes of HGF networks.
method Introduced a modified quadratic approximation to variational energy.
result Robust update equations across parameter space that track posterior faithfully.
A new GAN method ensures unbiased updates towards the steepest descent direction.
problem GANs update generator parameters in non-optimal directions.
method Introduces a theoretical framework and divergence approximating Wasserstein distance, ensuring unbiased steepest descent updates.
result Sets a new state-of-the-art on language generation tasks.
Algorithm estimates bounds of updated classifier coefficients efficiently.
problem Determining sensitivity of updated classifiers without retraining.
method Proposes an algorithm to estimate upper and lower bounds of updated classifier coefficients.
result Estimates bounds with low computational complexity and tightness.
Develops efficient method for updating models with small data changes.
problem Efficiently updating models when data changes (e.g., adding/removing instances/features).
method Generalized Low-Rank Update (GLRU) for non-linear estimators.
result Provides updated solutions with computational complexity proportional to dataset changes.
Paper studies efficient regression for dynamic graphs.
problem Regression over dynamic graphs.
method Update-efficient matrix embedding, O(nm) time complexity for updates.
result Exact optimal solution can be updated efficiently in dynamic graphs.
Analysis of model updates reveals sensitive data leaks.
problem Information leakage during model updates.
method Differential analysis of language model snapshots.
result New metrics (differential score, differential rank) reveal sensitive data leaks.
A new method improves few-shot image classification by updating top layers.
problem Few-shot image classification with limited data.
method Layer-wise adaptive updating (LWAU) for meta-learning.
result LWAU outperforms existing methods with a clear margin and learns more efficiently.
A new method for efficient neural network fine-tuning using queryable low-rank update atoms.
problem Rigidity of static low-rank adaptation methods when input and depth-wise computation vary.
method A shared queryable memory of low-rank update atoms, allowing dynamic and context-sensitive adaptation.
result Improves final test performance and training stability compared to standard low-rank adaptation.
Study on homogeneous geodesics in sub-Riemannian geometry.
problem Characterizing and understanding homogeneous geodesics in sub-Riemannian manifolds.
method Criterion for geodesics to be homogeneous, proof of geodesic orbit spaces, examples of geodesic orbit sub-Riemannian manifolds.
result Existence of at least one homogeneous geodesic under broad conditions.
The paper develops efficient algorithms for solving complex problems using coordinate updates.
problem Solving large or high-dimensional datasets with linear and nonlinear mappings.
method Develops coordinate-friendly operators and algorithms for various applications.
result New algorithms for machine learning, image processing, and optimization problems.
In non-compact manifolds, geodesic flowers exist.
problem Existence of geodesic flowers in non-compact manifolds.
method Proving the existence of non-trivial geodesic flowers in complete non-compact manifolds with locally convex ends.
result Non-trivial geodesic flowers exist in every complete non-compact manifold with locally convex ends.
In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for L2,1 norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix L2,1 norm minimization with…
Study examines auditing fairness in evolving models, identifying strategic updates that preserve audit properties.
problem Auditing fairness in machine learning models that adapt to changing environments.
method Characterizes strategic updates that preserve audit properties, proposes a generic PAC auditing framework.
result Establishes distribution-free auditing bounds for statistical parity using the SP dimension.
Drop-Muon updates only some layers, speeding up training.
problem Conventional deep learning optimizers update all layers at once, which can be inefficient.
method Drop-Muon updates only a subset of layers per step, with randomized schedules.
result Drop-Muon achieves up to 1.4x faster training time with similar accuracy.
This work analyzes how often to update the target network in Q-learning.
problem Understanding the optimal frequency of target network updates in Q-learning.
method Formulated target updates as a nested optimization scheme, derived finite-time convergence analysis.
result Optimal target update frequency increases geometrically over time.
Deep networks trained with Hebbian updates perform similarly to back-propagation on image datasets.
problem Training deep networks with realistic asymmetric connections and updates.
method Use Hebbian updates with separate feedforward and feedback weights, and local rule for updates.
result Similar performance to back-propagation achieved with Hebbian updates on challenging image datasets.
Study on Mabuchi functional's convexity using ε-geodesics.
problem Understanding the convexity of the Mabuchi functional.
method Analysis of ε-geodesics to study the Mabuchi functional's convexity.
result Uniform fiberwise non-degeneracy of geodesics when Mabuchi functional is ε-affine.
Locally extremal geodesic loops are closed geodesics in Riemannian manifolds.
problem Characterizing geodesic loops in Riemannian manifolds.
method Analyzing properties of geodesic loops and their conjugate points.
result Locally extremal non-self-conjugate geodesic loops are closed geodesics.
Geodesic graphs for special Finsler metrics on spheres are studied.
problem Characterizing geodesic orbit Finsler metrics on spheres.
method Explicit constructions and group extensions.
result Not all projective spaces admit invariant Finsler metrics.
The paper introduces geodesic φ-convex functions and their properties.
problem Generalizing geodesic functions to φ-convex functions.
method Introducing geodesic φ-convex functions and investigating their properties.
result Characterization of geodesic φ-convex functions via their φ-epigraphs.
Defines new geodesic semilocal E-preinvex functions and studies their properties.
problem Defines new functions to generalize existing convex and preinvex concepts.
method Introduces geodesic semilocal E-preinvex functions and proves their properties.
result Establishes sufficient optimality conditions for nonlinear fractional multiobjective programming.